Problem: Subtract $9a^2-6a+5$ from $10a^2+3a+25$.
Answer: Since we are asked to subtract $9a^2-6a+5$ from $10a^2+3a+25$, let's rewrite it as one expression. But how do we know which terms go where? Well, if we were asked to "subtract $9$ from $5$ ", we would rewrite it as $5 - 9$. In other words, we would start with $5$ and then subtract $9$. Let's use this pattern to rewrite the problem as one expression: ${(10a^2+3a+25)-(9a^2-6a+5)}$ Since we are subtracting, it is helpful to distribute the $\text{{negative sign}}$ across all terms in the second trinomial: $\begin{aligned}&(10a^2+3a+25){-}(9a^2-6a+5)\\ \\ =&(10a^2+3a+25){-}9a^2{-}(-6a){-}5\\ \\ =&10a^2+3a+25-9a^2+6a-5 \end{aligned}$ Note that the parentheses around the first trinomial don't affect the order of operations, so we can just remove them. When we add or subtract terms in a polynomial expression, the only way that we can simplify the expression is by combining those terms that are alike. Our expression contains terms of $3$ different degrees in the same variable: ${a^2}, {a},$ and the $\text{{constant}}$ term: ${{10a^2} {+3a} {+25} {-9a^2} {+6a} {-5}}$ Now that we have identified like terms, let's combine them. Make sure to keep track of positive and negative signs! ${{(10-9)a^2} + {(3+6)a} + {(25-5)}}$ When we combine the coefficients in front of each term, we get the following trinomial: ${a^2+9a+20}$